Degree-diameter problem $N(7,5)$
The largest possible number of vertices in a graph of maximum degree $7$ and diameter at most $5$.
Lower bound:
$2810$
Upper bound:
Unknown
Verified bounds
Verified bounds come with a certificate that is checked automatically: a formal proof in Lean, or an explicit construction checked by a program. Submit a certificate.
- Lower bound: None yet
- Upper bound: None yet
Updates from the literature
-
1994-10
Lower bound: $2756$
Dinneen, M. J., & Hafner, P. R. (1994). New results for the degree/diameter problem. Networks, 24(7), 359-367.
[via Table of the largest known graphs of a given diameter and maximal degree - Wikipedia] -
2026-10
Lower bound: $2810$
Dharunish Yugeswardeenoo in October 2026
[via Comellas, F. The (Degree, Diameter) Problem for Graphs (records table), last changed November 2, 2026]